The announcement came in the discussion paper, The Governance of Britain, presented to Parliament yesterday by the new Prime Minister.
It says the Government will work with the Charity Commission, Capacitybuilders and sector leaders to explore the options for "enabling charities and other sector organisations to better campaign on issues that are likely to advance the cause of the purposes for which they have been established."
The green paper says it will consider the recommendations of the independent Advisory Group on Campaigning and the Voluntary Sector, chaired by Baroness Helena Kennedy.
The group's report, published in May, recommends that charities should be permitted to direct all their resources towards political campaigning, rather than having to keep such activities as "ancillary" to their main activities.
It also recommends an overhaul of the Communications Act 2003 and the Serious Organised Crime and Police Act 2005, which limits demonstrations near Parliament.
The announcement appears to confirm Baroness Kennedy's claim that Brown becoming Prime Minister would be one of a number of "key moments" which campaigners could seize to shape the future political landscape.
Baroness Kennedy said: "I am really pleased that the Government has recognised the need for some reform in relation to the law on campaigning, and this is an opportunity for the charity sector to engage in am important debate."
The green paper says that while public engagement with the formal political process has dwindled, the numbers of people who are members of pressure groups or prepared to sign petitions have grown.
The paper reads: "Third sector campaigning organisations, such as Make Poverty History, play an ever more important role in driving social, economic and environmental change. In this context, it is important to ensure that the regulatory framework for the third sector, together with the Government's consultation mechanisms and investments in strengthening the organisational capacity of the sector, help it to foster and harness community voices on important issues of public policy."